If you're serious and don't know where your free Destroyer is, you go to the shipyard of your race, and pick it from the list. If for some reason you do not have the token to get it, there is a dialog option from one of the shipyard NPCs to claim another token.
First, I want to say that I bought a LTS back before launch and at this point the LTS has payed for itself before F2P even hit. Right now I effectively get a free zen stipend every month for that early contribution.
There are many benefits to having a LTS but many of those same benefits you can get by purchasing them separately. The best way to see if it is worth it to you is to tally up the cost of buying what you want via zen store versus a LTS.
It is a long term investment not something you buy for a short stint. Make sure the benefits match up with what you are looking for then decide. Anyone can buy a LTS but not everyone would get their money's worth back.